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Saumyojit

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One fashion house has to make 810 dresses and another one, 900 dresses during the same period of time. in the first house, the order was ready 3 days ahead of time and in the second house, 6 days ahead of time. how many dresses did each fashion house make a day if the second house made 21 dresses more a day than the first?



Description of variables : Wa = Original work rate of first fashion house
Wd = Original work rate of second fashion house .
Wb and Wc are the increased work rates of respective houses

Days = No of days reqd for completing work in original work rate of first house
Days 2 = No of days reqd for completing work in original work rate in 2nd house

Equations:

Wa * Days = 810 ---(i)

Wb * (Days -3) = 810 --(ii)

Wc * Days2 = 900 ---(iii)

Wd * (Days2 - 6) = 900 ---(iv)


second house made 21 dresses more a day than the first

Wd = Wb + 21 --(v)


Substituting Wb + 21 in place of Wd in (iv)

(Wb + 21) * (Days2 -6) = 900

(Days2 -6) = 900 / (Wb + 21)





from eqn (ii)
=> Wb * (Days -3) = 810 => Wb = 810 / (Days - 3)

from eqn (ii) we also get
=> Days = (810 / Wb ) + 3



From eqn(iv) Wd * (Days2 - 6) = 900 , we get

(Wb + 21 ) * (Days2 - 6) = 900

( ( 810 / (Days -3) + 21 ) * ( Days2 -6) = 900

So 900 = ( ( 810 / (Days -3) + 21 ) * ( Days2 -6)



From eqn(iv) we also get
Days2 = 900 / (Wb + 21) + 6


SOLVING :

Substituting 900 in eqn(iii)

Wc * Days2 = ( ( 810 / (Days -3) + 21 ) * ( Days2 -6) ) ) / (Days -3)

900 = ( ( ( 810 / (Days -3) + 21 ) * ( Days2 -6) ) / (Days -3)

Now i would bring in Wb in place of Days as I want to find Wb on solving the above equation


900= ( 810 ( Days2 -6) + 21 * (810 /Wb + 3) * (Days2 - 6 ) - 63( Days2 - 6) ) / ( (810 / Wb) + 3 - 3 )

Now like this i also substituted Days2 with Wb ,

So it stands like this

900= ( (729 * 10^3) / (WB + 21) + 17010/ Wb * ( 900/(Wb + 21) + 6 ) + 63 * ( 900 /(Wb + 21) + 6) - (102060 /Wb ) - 378 - 63 * ( 900/ (Wb + 21) + 6 ) + 378 ) / ( 810 / Wb)


10Wb / 9 = 729000 / (Wb + 21) + 15309000 / (Wb (Wb + 21) )

10Wb^3 + 210Wb^2 = 6561000Wb + 137781000

Wb = ...


Is the approach correct?
 
Where do Wc and Wd come from? I did not notice anything about "increased" vs. "original" work rates in the problem's statement.
 
blamocur said:
Where do Wc and Wd come from? I did not notice anything about "increased" vs. "original" work rates in the problem's statement.
Click to expand...
the order was ready 3 days ahead of time and in the second house, 6 days ahead of time .

It means that the order of the first house and the order of the second house was meant to be completed in some no of days respectively but it was completed ahead of time . So obviously There's a original work rate of the two houses and after increase in efficiency there is a new work rate .

where is my logic wrong ?
 
Saumyojit said:
the order was ready 3 days ahead of time and in the second house, 6 days ahead of time .

It means that the order of the first house and the order of the second house was meant to be completed in some no of days respectively but it was completed ahead of time . So obviously There's a original work rate of the two houses and after increase in efficiency there is a new work rate .

where is my logic wrong ?
Click to expand...
Nothing wrong with your logic, but I don't see the need for 6 variables there. I should have asked "why do you need Wa and Wd?" instead. Also, is "Days2" different from "Days" ? I can see a system of 3 equations with 3 variables so far.
 
Saumyojit said:
Days2 is obviously different from Days. One is for the original work rate and another is for the increased work rate .


are those 3equations covered in my six equations .
Click to expand...
They are in (i), (ii) and, once you fix a minor error there, (v)
 
Saumyojit said:
One fashion house has to make 810 dresses and another one, 900 dresses during the same period of time. in the first house, the order was ready 3 days ahead of time and in the second house, 6 days ahead of time. how many dresses did each fashion house make a day if the second house made 21 dresses more a day than the first?
Click to expand...
Let that time = D days

900/(D-6) - 810/(D-3) = 21 ..........................................................why?

D = ?

Continue.....
 
Saumyojit said:
Wa * Days = 810 ---(i)

Wb * (Days -3) = 810 --(ii)

Wc * Days2 = 900 ---(iii)

Wd * (Days2 - 6) = 900 ---(iv)


What error?

Please solve it .
Click to expand...
I am not going to solve it for you, but will be happy to help you solve it.

You don't need Wa, Wd and Days2, only Wb, Wc and 'Days' (I'd abbreviate it to 'D', but this is a matter of style). But please revisit your equations and find several errors there.
 
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